Split blocks in block-based mesh
Remeshing creates no subdivision of volume, just a sampled surface.

There is a 'Grid' option in particle systems, that enables you to set a resolution of the grid intersections, and the size of the objects placed on them. 

If, rather than re-meshing, you make your object into a particle emitter from volume,  and set a cube as the particle dupli-object, you can voxelize it.

In the example here, (we're on frame 1 in the timeline)  Suzanne is the emitter, and a cube is duplicated to the particle system. All the other particle settings are at their defaults.



If you go to Suzanne's modifier stack, and hit 'Convert' on the particle system, the particles become real instances of the cube. Here I've scaled out all the positions of the cubes so you can see the inside ones...



In the Particles > Emission panel, the 'Resolution' setting divides the longest side of the bounding box of the emitter, and the 'Size' field of the Particles > Render panel will scale the cube-dupli.. (probably best set to 1).

So to make your voxels exactly fill an emitter whose bounding-box longest side is 3.5, with Resolution set to 10, and Size set to 1, your cube would have to be 0.35 on the side.